{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:M3AMSHTJQP3ZE2N2KISJXNB3PR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1817dee10a06f86085bbad0f6542b9b70209e4e756b30b9e12866ef334526359","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2016-09-26T16:18:40Z","title_canon_sha256":"8dfc1b40490eeecb277e9e4bc81ca240c1a13cc47f6b83b63d30134079efd767"},"schema_version":"1.0","source":{"id":"1611.02655","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.02655","created_at":"2026-05-18T00:59:51Z"},{"alias_kind":"arxiv_version","alias_value":"1611.02655v1","created_at":"2026-05-18T00:59:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.02655","created_at":"2026-05-18T00:59:51Z"},{"alias_kind":"pith_short_12","alias_value":"M3AMSHTJQP3Z","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"M3AMSHTJQP3ZE2N2","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"M3AMSHTJ","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:718c06384b4863dcebd89a09a422691ef637cc35e24a59039449c651aa3f2708","target":"graph","created_at":"2026-05-18T00:59:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In graph signal processing, the graph adjacency matrix or the graph Laplacian commonly define the shift operator. The spectral decomposition of the shift operator plays an important role in that the eigenvalues represent frequencies and the eigenvectors provide a spectral basis. This is useful, for example, in the design of filters. However, the graph or network may be uncertain due to stochastic influences in construction and maintenance, and, under such conditions, the eigenvalues of the shift matrix become random variables. This paper examines the spectral distribution of the eigenvalues of","authors_text":"Jose M. F. Moura, Stephen Kruzick","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2016-09-26T16:18:40Z","title":"Spectral Statistics of Lattice Graph Percolation Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02655","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:268e62ef89bd473b4ff8e11cf30203ab32c8c6b02e2cf81f31548c4be172b465","target":"record","created_at":"2026-05-18T00:59:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1817dee10a06f86085bbad0f6542b9b70209e4e756b30b9e12866ef334526359","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2016-09-26T16:18:40Z","title_canon_sha256":"8dfc1b40490eeecb277e9e4bc81ca240c1a13cc47f6b83b63d30134079efd767"},"schema_version":"1.0","source":{"id":"1611.02655","kind":"arxiv","version":1}},"canonical_sha256":"66c0c91e6983f79269ba52249bb43b7c5cd39c24e35788428050013050e0f783","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66c0c91e6983f79269ba52249bb43b7c5cd39c24e35788428050013050e0f783","first_computed_at":"2026-05-18T00:59:51.311798Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:51.311798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0sewf0o+iZIgzzzF65JHLHq58yPa1Ueya0qilltjxS7ND5TUPbC1HijllGJEpqRoFbKmCWfz/MT2YWW+qbe4CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:51.312284Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.02655","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:268e62ef89bd473b4ff8e11cf30203ab32c8c6b02e2cf81f31548c4be172b465","sha256:718c06384b4863dcebd89a09a422691ef637cc35e24a59039449c651aa3f2708"],"state_sha256":"42b578d3895fb28d9bb2521d50871ce94bd021f2d2f16f0e383acc18d4e04f02"}